Entanglement and Yangian in a \({V^{\otimes 3}}\) Yang-Baxter system. (English) Zbl 1239.81028
Summary: In this paper, a \(8 \times 8\) unitary Yang-Baxter matrix \({\breve{R}_{123}(\theta_{1},\theta_{2},\phi)}\) acting on the triple tensor product space, which is a solution of the Yang-Baxter Equation for three qubits, is presented. Then quantum entanglement and the Berry phase of the Yang-Baxter system are studied. The Yangian generators, which can be viewed as the shift operators, are investigated in detail. And it is worth mentioning that the Yangian operators we constructed are independent of choice of basis.
MSC:
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81Q70 | Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory |
| 16T25 | Yang-Baxter equations |
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